Journal of Geometry and Physics最新文献

{"title":"Field theory via higher geometry I: Smooth sets of fields","authors":"Grigorios Giotopoulos ,&nbsp;Hisham Sati","doi":"10.1016/j.geomphys.2025.105462","DOIUrl":"10.1016/j.geomphys.2025.105462","url":null,"abstract":"<div><div>Most modern theoretical considerations of the physical world suggest that nature is at a minimum: (1) field-theoretic, (2) smooth, (3) local, (4) gauged, (5) containing fermions, and last but not least: (6) non-perturbative. Tautologous as this may sound to experts of the field, it is remarkable that the mathematical notion of geometry which reflects <em>all</em> of these aspects – namely, as we will explain: “<em>supergeometric homotopy theory</em>” – has received little attention even by mathematicians and remains unknown to most physicists. Elaborate algebraic machinery is known for <em>perturbative</em> field theories both at the classical and quantum level, but in order to tackle the deep open questions of the subject, these will need to be lifted to a global geometry of physics. Prior to considering any notion of non-perturbative quantization procedure, by necessity, this must first be accomplished at the classical and pre-quantum level.</div><div>Our aim in this series is, first, to introduce inclined physicists to this theory, second to fill mathematical gaps in the existing literature, and finally to rigorously develop the full power of supergeometric homotopy theory and apply it to the analysis of fermionic (not <em>necessarily</em> super-symmetric) field theories. Secondarily, this will also lead to a streamlined and rigorous perspective of the type that we hope would also be desirable to mathematicians.</div><div>In this first part, we explain how classical bosonic Lagrangian field theory (variational Euler-Lagrange theory) finds a natural home in the “topos of smooth sets”, thereby neatly setting the scene for the higher supergeometry discussed in later parts of the series. This introductory material will be largely known to a few experts but has never been comprehensively laid out before. A key technical point we make is to regard jet bundle geometry systematically in smooth sets instead of just its subcategories of diffeological spaces or even Fréchet manifolds – or worse simply as a formal object. Besides being more transparent and powerful, it is only on this backdrop that a reasonable supergeometric jet geometry exists, needed for satisfactory discussion of any field theory with fermions.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105462"},"PeriodicalIF":1.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spinors and the Descartes circle theorem","authors":"Daniel V. Mathews ,&nbsp;Orion Zymaris","doi":"10.1016/j.geomphys.2025.105458","DOIUrl":"10.1016/j.geomphys.2025.105458","url":null,"abstract":"<div><div>The classic Descartes circle theorem relates the curvatures of four mutually externally tangent circles, three “petal” circles around the exterior of a central circle, forming a “3-flower” configuration. We generalise this theorem to the case of an “<em>n</em>-flower”, consisting of <em>n</em> tangent circles around the exterior of a central circle, and give an explicit equation satisfied by their curvatures. The proof uses a spinorial description of horospheres in hyperbolic geometry.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105458"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rigidity results for compact biconservative hypersurfaces in space forms","authors":"Ştefan Andronic ,&nbsp;Aykut Kayhan","doi":"10.1016/j.geomphys.2025.105460","DOIUrl":"10.1016/j.geomphys.2025.105460","url":null,"abstract":"<div><div>In this paper we present alternative proofs for two known rigidity results concerning non-negatively curved compact biconservative hypersurfaces in space forms. Further, we prove some new rigidity results by replacing the hypothesis of non-negative sectional curvature with some estimates of the squared norm of the shape operator.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105460"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topological recursion and variations of spectral curves for twisted Higgs bundles","authors":"Christopher Mahadeo ,&nbsp;Steven Rayan","doi":"10.1016/j.geomphys.2025.105459","DOIUrl":"10.1016/j.geomphys.2025.105459","url":null,"abstract":"<div><div>Prior works relating meromorphic Higgs bundles to topological recursion, in particular those of Dumitrescu-Mulase, have considered non-singular models that allow the recursion to be carried out on a smooth Riemann surface. We start from an <span><math><mi>L</mi></math></span>-twisted Higgs bundle for some fixed holomorphic line bundle <span><math><mi>L</mi></math></span> on the surface. We decorate the Higgs bundle with the choice of a section <em>s</em> of <span><math><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>⊗</mo><mi>L</mi></math></span>, where <em>K</em> is the canonical line bundle, and then encode this data as a <em>b</em>-structure on the base Riemann surface which lifts to the associated Hitchin spectral curve. We then propose a so-called twisted topological recursion on the spectral curve, after which the corresponding Eynard-Orantin differentials live in a twisted cotangent bundle. This formulation retains, and interacts explicitly with, the singular structure of the original meromorphic setting — equivalently, the zero divisor of <em>s</em> — while performing the recursion. Finally, we show that the <span><math><mi>g</mi><mo>=</mo><mn>0</mn></math></span> twisted Eynard-Orantin differentials compute the Taylor expansion of the period matrix of the spectral curve, mirroring a result of Baraglia-Huang for ordinary Higgs bundles and topological recursion. Starting from the spectral curve as a polynomial form in an affine coordinate rather than a Higgs bundle, our result implies that, under certain conditions on <em>s</em>, the expansion is independent of the ambient space <span><math><mtext>Tot</mtext><mo>(</mo><mi>L</mi><mo>)</mo></math></span> in which the curve is interpreted to reside. While our focus is almost exclusively geometric, we include some preliminary thoughts on connections to questions in theoretical condensed matter physics.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105459"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-Einstein structures on f-associated standard static space-time","authors":"Sameh Shenawy ,&nbsp;Uday Chand De ,&nbsp;Ibrahim Mandour ,&nbsp;Nasser Bin Turki","doi":"10.1016/j.geomphys.2025.105463","DOIUrl":"10.1016/j.geomphys.2025.105463","url":null,"abstract":"<div><div>In a generalized quasi-Einstein <em>f</em>-associated standard static space-time, the Laplacian Δ of the warping function <em>f</em> adheres to the Laplacian equation. The Ricci tensor of the base manifold satisfies the generalized Ricci-Hessian equation. The base manifold is shown to be quasi-Einstein if the Hessian <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msup></math></span> of the warping function <em>f</em> is proportional to the metric tensor, and it is proven to be a generalized quasi-Einstein manifold if <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msup></math></span> takes on the form of a perfect fluid tensor. The scalar curvature of both the space-time and its base manifold are provided. The Ricci curvature of the base manifold, the Laplacian of the warping function and the scalar curvature of the base manifold in a quasi-Einstein <em>f</em>-associated SSST are described in two scenarios: when the generator is space-like and when it is time-like. In the first scenario, it is demonstrated that the space-time is Ricci simple and the warping function remains constant if the base manifold is constant. In a generalized quasi-Einstein standard static space-time, the base manifold is a generalized quasi-Einstein manifold if the Hessian <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msup></math></span> is proportional the metric tensor. A specific example of an <em>f</em>-associated standard static space-time is also provided. The equation of state takes the form <span><math><mi>p</mi><mo>=</mo><mi>w</mi><mi>σ</mi></math></span> where <em>w</em> ranges from −1 to 0, representing a transition from dark energy-dominated space-times to non-relativistic, matter-dominated ones.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105463"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cocommutative connected vertex (operator) bialgebras","authors":"Yukun Xiao ,&nbsp;Jianzhi Han","doi":"10.1016/j.geomphys.2025.105461","DOIUrl":"10.1016/j.geomphys.2025.105461","url":null,"abstract":"<div><div>In this paper, by the equivalence between the category of Lie conformal algebras and the category of cocommutative connected vertex bialgebras, which was obtained in <span><span>[8]</span></span>, we classify simple objects in the latter category. We introduce the notion of Lie conformal operator algebra and the notion of vertex operator bialgebra. And it is shown that the category of Lie conformal operator algebras and the category of cocommutative connected vertex operator bialgebras are equivalent.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105461"},"PeriodicalIF":1.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blobbed topological recursion from extended loop equations","authors":"Alexander Hock ,&nbsp;Raimar Wulkenhaar","doi":"10.1016/j.geomphys.2025.105457","DOIUrl":"10.1016/j.geomphys.2025.105457","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider the &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; Hermitian matrix model with measure &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;exp&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mi&gt;tr&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the Gaußian measure with covariance &lt;span&gt;&lt;math&gt;&lt;mo&gt;〈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;〉&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt; for given &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. It was previously understood that this setting gives rise to two ramified coverings &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of the Riemann sphere strongly tied by &lt;span&gt;&lt;math&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and a family &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; of meromorphic differentials conjectured to obey blobbed topological recursion due to Borot and Shadrin. We develop a new approach to this problem via a system of six meromorphic functions which satisfy extended loop equations. Two of these functions are symmetric in the preimages of &lt;em&gt;x&lt;/em&gt; and can be determined from their consistency relations. An expansion at ∞ gives global linear and quadratic loop equations for the &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;. These global equations provide the &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; not only in the vicinity of the ramification points of &lt;em&gt;x&lt;/em&gt; but also in the vicinity of all other poles located at opposite diagonals &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105457"},"PeriodicalIF":1.6,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infinitesimal 2-braidings from 2-shifted Poisson structures","authors":"Cameron Kemp,&nbsp;Robert Laugwitz,&nbsp;Alexander Schenkel","doi":"10.1016/j.geomphys.2025.105456","DOIUrl":"10.1016/j.geomphys.2025.105456","url":null,"abstract":"<div><div>It is shown that every 2-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra <em>A</em> defines a very explicit infinitesimal 2-braiding on the homotopy 2-category of the symmetric monoidal dg-category of finitely generated semi-free <em>A</em>-dg-modules. This provides a concrete realization, to first order in the deformation parameter <em>ħ</em>, of the abstract deformation quantization results in derived algebraic geometry due to Calaque, Pantev, Toën, Vaquié and Vezzosi. Of particular interest is the case when <em>A</em> is the Chevalley-Eilenberg algebra of a Lie <em>N</em>-algebra, where the braided monoidal deformations developed in this paper may be interpreted as candidates for representation categories of ‘higher quantum groups’.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105456"},"PeriodicalIF":1.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Additional symmetries for the N=2 supersymmetric Two-Boson hierarchy and the multi-component generalization","authors":"Jian Li ,&nbsp;Chuanzhong Li","doi":"10.1016/j.geomphys.2025.105455","DOIUrl":"10.1016/j.geomphys.2025.105455","url":null,"abstract":"<div><div>In this paper, we primarily define the N=2 supersymmetric Two-Boson integrable system using N=2 quantum superfields and introduce time variables derived from a non-abelian Lie superalgebra. We construct additional symmetries for the N=2 supersymmetric Two-Boson hierarchy through the Orlov-Schulman operator, which depend on the time variables and the dressing operator. Furthermore, we establish a relationship between the supersymmetric integrable system of N=2 quantum superfields and the Lie superalgebra. Finally, we extend the N=2 supersymmetric Two-Boson hierarchy to the multi-component case and construct the corresponding additional symmetries for it.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"211 ","pages":"Article 105455"},"PeriodicalIF":1.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Separation of variables for the Clebsch model: so(4) spectral/separation curves","authors":"T. Skrypnyk","doi":"10.1016/j.geomphys.2025.105453","DOIUrl":"10.1016/j.geomphys.2025.105453","url":null,"abstract":"<div><div>In the present paper we construct symmetric separation of variables (SoV) for the anisotropic Clebsch model for which both curves of separation coincide with spectral curve <span><math><mi>K</mi></math></span> of its <span><math><mi>s</mi><mi>o</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span>-valued Lax matrix. We explicitly construct coordinates and momenta of separation, Abel-type quadratures and reconstruction formulae for the presented new SoV. The found SoV is the first example of SoV for integrable systems with generic <span><math><mi>s</mi><mi>o</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-valued Lax matrices when all curves of separation coincide with a spectral curve of the corresponding <span><math><mi>s</mi><mi>o</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-valued Lax matrix and <span><math><mi>n</mi><mo>&gt;</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105453"},"PeriodicalIF":1.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}